Finite element studies of quantum dots

Abstract

The time-independent Schrödinger equation is solved using the finite element method (FEM) and the finite difference method (FDM). The resulting eigenvalue problems are solved using the ARPACK++ library. Both methods are implemented in the same program so the methods can be compared. The program is limited to spherically symmetric potentials.

We study a quantum system of two electrons in a harmonic oscillator potential and a constant magnetic field. This system is an approximation to the two-electron quantum dot. By a coordinate transformation this equation can be separated into two independent single-particle equations, which we can solve in the same program.